Resource allocation with partial responsibilities for initial endowments

• DOI: http://doi.org/10.1111/ijet.12133
• Published date: 01 December 2017
• Author: Christopher P. Chambers,Takashi Hayashi
• Date: 01 December 2017

doi: 10.1111/ijet.12133

Resource allocation with partial responsibilities for initial

endowments

Christopher P. Chambers∗and Takashi Hayashi†

This paper studies a resource allocation problem in which each individual is responsible but

in general only partially for his initial endowment. We consider pure-exchangeeconomies with

initial endowments but we do not assume the individual rationality axiom, taking the society

to consist of citizens who cannot opt out of it. Wecharacterize a class of allocation rules which

are parametrized by income redistribution codes. In particular,we characterize a one-parameter

family of income redistribution codes, in which one extreme corresponds to the case where

everybody is 100% responsible for his initial endowment and the other extreme corresponds to

the case where nobody is responsible for his endowment at all.

Key wor ds resource allocation, partial responsibility, incomeredistr ibution code

JEL classification D50, D60, D70

Accepted 12 July2016

1 Introduction

This paper studies a resource allocation problem in which each individual is responsible but in

general only partially for his initial endowment.

Existing normative and axiomatic studies on resource allocation assume either that everybody is

100% responsible for his initial endowment, or that any such notion of individual responsibility or

entitlement is irrelevant. The former line of thought assumes that nobody should get worse off than

his initial endowment (individual rationality) and characterizes the Walras rule (see, for example,

Hurwicz 1979; Gevers 1986; Thomson 1979; Nagahisa 1991; Nagahisa and Suh 1995). This line of

thought imagines that individuals are entirely responsible for their endowment. In contrast, the

latter line of research imagines individuals are not at all responsible for their endowment. This is

reflected in the assumption that only the aggregate endowment matters; the additional imposition of

equity axioms typically characterizes the Walras rule starting from equal division (see, for example,

Nagahisa and Suh 1995; Thomson 1988; Thomson and Zhou 1993).

In this paper,we imagine that a social planner need not restrict herself to either of these two ideas;

she may have a different idea of how responsible each agent is for his endowment. To this end, we

study a family of rules that allows flexibility in the degree of responsibility. Our main contribution

is to derive a parametric family of such rules, which form compromises between the previously

discussed families. In order to meaningfully discuss a parametric notion of responsibility, our notion

∗Department of Economics, Georgetown University,Washington DC, USA.

†Adam Smith Business School, Universityof Glasgow, Glasgow, Scotland, UK. Email: takashi.hayashi@glasgow.ac.uk

Wethank the anonymous referee for helpful comments and suggestions which improved the paper substantially, as well

as for finding errors and gaps in the previous versions.

International Journal of Economic Theory 13 (2017) 355–368 © IAET 355